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&[DATE] &[TIME] - &[FILENAME]

The cubic spline modeling "Curvator"

t0 1 time :

Inspired/adapted from Paul R. Lorczak [Mathsoft]

Point(s) spec's algo data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

Sampled data to fit data 0.192 0.217 0.224 0.07 0.256 0.185 0.288 0.434 0.32 0.689 0.352 0.822 0.385 0.705 0.417 0.359 0.449 0.418 0.481 0.711 0.513 0.94 0.545 1 0.577 0.932 0.609 0.775 0.641 0.566 0.673 0.346 0.706 0.154 0.738 0.028 0.77 0.00694 0.802 0.13 202 mat :

Curvature at
calib'n points Deriv 10 - 15 - 6.5 6.5 41 mat :

Calibration points XY 0.192 0.2174 0.4 0.52174 0.5 0.87 0.8018 0.1304 42 mat :

X XY 1 col :

Y XY 2 col :

x X :

y Y :

Linear solving the system S j 13 range algo 1 j el x j el (3^x j el (2^x j el 1 x j 1 + el (3^x j 1 + el (2^x j 1 + el 13 x j el (2^* 2 x j el * 103 x j 1 + el (2^* 2 x j 1 + el * 1044 mat (1 -^y j el y j 1 + el Deriv j el Deriv j 1 + el 41 mat * : for algo 21 line :

algo #

Smath does NOT take the col assignments .... col(S,#) neither from file write/read

S 645.487 - 561.173 154.105 - 13.687 41 mat 1546.52 - 2195.302 1028.912 - 159.816 41 mat 196.537 383.778 - 242.875 49.19 - 41 mat 13 mat

t s3 S 3 el t 3^t 2^t 114 mat transpose * :

a b c spec . 12 black 13 mat :

t s2 S 2 el t 3^t 2^t 114 mat transpose * :

Data data a b c spec pts :

a b c spec + 14 red 13 mat :

t s1 S 1 el t 3^t 2^t 114 mat transpose * :

calib XY a b c spec pts :

Piecewise construct t Spline t 0.5 ≥ t s3 t 0.4 ≥ t s2 t s1 if if :

t x 3 el ≥ rejected ≡

The modeling "Curvator" passes through the XY's support points. The remaining of the shape is achieved by the slope [Deriv] @ support points associated with the linear solver. The data points can be noisy, this is a manual data fitter. This demo results from a real noisy project from which a smooth fitted 20 data points were collected [Mathsoft Collaboratory].

Discretise/collect the project Spline u 0.180 0.820 0.181 range : i 1 u rows range u i el u i el : v i el u i el Spline eval : 21 line for u v augment 31 line :

The "Curvator" adjusted by hand

Spline Data calib 3 1 sys

1 time t0 - 1.7 sec *